Experimental and theoretical work has shown that for each of the fundamental particles such as proto — Physical Chemistry — Electrochemistry Chemistry Question
Proton – antiproton atom
Experimental and theoretical work has shown that for each of the fundamental particles such as protons (p) and electrons (e) there exist antiparticles which differ from their counterparts usually in one property only, but have the same mass. Antielectrons (or positrons) are positively charged, whereas antiprotons ( p ) are negatively charged. Antimatter composed of antiparticles had not been observed until very recently. Antihydrogen consisting of positrons attached to antiprotons was created in laboratories in 2002 (Nature 419, 456 (2002)). An even more exotic form of an atom would consist of a combination of a proton and an antiproton (pp ).
Assuming that the pp atom is hydrogen–like, calculate:
i) what is its ionization energy and its Bohr radius,
ii) what is the wavelength of the transition from the ground electronic state to the first excited state.
Model Answer
i)
We can use the expression for hydrogen–like atoms to calculate the energy levels.
where Z is the total number of charges in the nucleus (= 1), e is the electron charge (1.6022×10–19 C), μ is the reduced mass of the system with µ = (m1−1 + m2−1)−1 and m1 = m2 = mp = 1.6726×10–27 kg, thus μ = ½ mp, ε0 is the permittivity of vacuum (= 8.8542×10–12 C2 J–1 m–1) , h is the Planck constant (= 6.626076×10–34 J s) and n is the principal quantum number of the system taking values 1, 2, …
The Bohr radius is given by ... which is 1836 / 2 times smaller than the hydrogen radius due to the difference in reduced mass of the "atom".
ii)
For n = 1, E1 = – 2.00129 × 10-15 J and for n = 2, E2 = ..., hence ΔE = E2 – E1 = 1.50097 × 10-15 J
ν = ΔE / h = 2.2652 × 10^18 s-1
λ = c / ν = 1.3234 × 10-10 m = 1.3234 Å